In the operation of a rotary offset printing press, freshly printed substrates such as sheets or web material are guided by transfer cylinders from one printing unit to another, and then they are delivered to a sheet stacker or to a sheet folder/cutter unit. Marking and smearing of the freshly printed sheets sometimes occur as follows. As each sheet is transferred from the impression cylinder, and after having received an inked image, the freshly printed sheet is immediately pulled along a reverse curvilinear path with its freshly printed side in contact with the sheet support surface of the transfer cylinder. Movement of the freshly printed sheet is so rapid that the ink on the sheet does not have time to set before it contacts the surface of the transfer cylinder; consequently, a portion of the wet ink accumulates on the transfer cylinder surface. As the next sheet and all subsequent sheets are transferred, they will be pulled into contact with the accumulated ink and thus will be marked or smeared.